Rest energy of 238Uranium and gamma factor

So, I know that for a certain Synchrotron I have an output value of 1.5GeV/u for Uranium-238 particles, with a charged state of 28+ (## ^{238}U^{+28} ##). For this ion I would like to calculate the rest energy and the associated relativistic gamma factor. My approach was the following:

Rest energy (ignoring the mass of electrons):

For the rest energy, I considered that Uranium-238 is made of 238 neutrons and protons in total, and I just multiplied this value by the atomic mass number:

Is this homework, or is it a real-world problem? If it's a real-world problem, can't you ask whoever you're working with whether they mean the total energy or just kinetic energy? If it's homework, please read this: https://www.physicsforums.com/help/homeworkhelp/

Your method of finding the rest mass is probably good to about 2 sig figs, but why not just look it up rather than trying to estimate it?

This is a real-world problem. But, unfortunately I have no access to the person who wrote this.
In reality, what I'm trying to figure out is the relation between these two numbers presented on a table for emittance in this synchrotron for the Uranium-238 ion:

εx (norm.) [mm mrad] = 32εx (phys.) [mm mrad] = 47

I thought that the number εx (phys.) would be the emittance, and εx (norm.) the normalized emittance, which are related by:

## \epsilon_{norm} = \gamma \beta \epsilon ##

So, I was trying to see if this is what they meant. But, my calculations for ## \gamma \beta ## for this ion don't match their ratio, which is around ## \gamma \beta = 32/47 = 0.681 ##.

Yes, your calculation of gamma looks right to me, if the given energy is total energy. If you interpret it as kinetic energy, the disagreement with the expected value of ##\gamma\beta## becomes worse, right?

Surely if you're working with a synchrotron you have access to accurate information about its energy...?

Staff: Mentor

That I know, the Synchrotron has a magnetic rigidity of 100 Tesla meter and the Dipole magnet field is around 2 Tesla with a curvature of around 50meter. But, how can I go from here to the values of emittance? These emittance values are on the output of the synchrotron.

Well, I just wanted to find out what exaclty do they mean by these different definitions of emittance they present on some tables: εx (norm.) [mm mrad] and εx (phys.) [mm mrad]

Staff: Mentor

If the 100 Tesla meter refer to the radius, the values are way off. For the circumference it would make sense.
The accelerator could run with a weaker field for your uranium, of course, then the design values don't help.